R Notebook

Q10 is aspirations

Q7_7_1 is javascript skills

Q7_7_2 is mashup skills

Q8_8_1 is general programming skills

# reading input 
df<-read.csv("input/commits_novelty.csv", header =TRUE, sep=",")
df <- df[complete.cases(df), ]  
df

df$group = factor(df$group)

# create new columns called log relational novelty
df$log_relational_novelty <- log(df$similarity+1) 
df$log_count <- log(df$count+1) 
df$Q7_Q7_1 <- log(df$Q7_Q7_1+1)
df$Q7_Q7_2 <- log(df$Q7_Q7_2+1)
df$Q8_Q8_1 <- log(df$Q8_Q8_1+1)
df$Q10 <- log(df$Q10+1)
df

# standardizing variables for skills and aspirations. 
cols <- c("Q7_Q7_1", "Q7_Q7_2", "Q8_Q8_1", "Q10", "log_relational_novelty", "log_count")
df[cols] <- scale(df[cols])
df

mod <- lm(log_count ~ factor(group), data=df)
summary(mod)

Call:
lm(formula = log_count ~ factor(group), data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.1938 -0.9742 -0.1165  0.5462  3.4873 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)  
(Intercept)    -0.07037    0.08193  -0.859   0.3907  
factor(group)1  0.21956    0.11368   1.931   0.0539 .
factor(group)2 -0.06328    0.11773  -0.537   0.5911  
factor(group)3  0.10161    0.11301   0.899   0.3689  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9968 on 607 degrees of freedom
Multiple R-squared:  0.01137,   Adjusted R-squared:  0.006485 
F-statistic: 2.327 on 3 and 607 DF,  p-value: 0.07358

mod <- lm( log_relational_novelty ~ Q10 + Q8_Q8_1 + Q7_Q7_1 + Q7_Q7_2, data = df)
summary(mod)

Call:
lm(formula = log_relational_novelty ~ Q10 + Q8_Q8_1 + Q7_Q7_1 + 
    Q7_Q7_2, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.1132 -0.4060  0.3574  0.7447  1.3212 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept) -4.765e-16  4.012e-02   0.000   1.0000  
Q10          1.517e-02  4.341e-02   0.349   0.7269  
Q8_Q8_1      8.695e-02  4.473e-02   1.944   0.0524 .
Q7_Q7_1     -6.090e-02  5.007e-02  -1.216   0.2243  
Q7_Q7_2      1.201e-01  5.134e-02   2.340   0.0196 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9918 on 606 degrees of freedom
Multiple R-squared:  0.02273,   Adjusted R-squared:  0.01628 
F-statistic: 3.524 on 4 and 606 DF,  p-value: 0.007427

mod <- lm( log_relational_novelty ~ log_count , data = df)
summary(mod)

Call:
lm(formula = log_relational_novelty ~ log_count, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.2833 -0.4112  0.2627  0.6549  1.4603 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.026e-16  3.743e-02    0.00        1    
log_count    3.816e-01  3.746e-02   10.19   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9251 on 609 degrees of freedom
Multiple R-squared:  0.1456,    Adjusted R-squared:  0.1442 
F-statistic: 103.8 on 1 and 609 DF,  p-value: < 2.2e-16

mod <- lm( log_relational_novelty ~ factor(group) + log_count + Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10 , data = df)
summary(mod)

Call:
lm(formula = log_relational_novelty ~ factor(group) + log_count + 
    Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.2898 -0.4308  0.2405  0.6320  1.4916 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)    -0.17946    0.07540  -2.380   0.0176 *  
factor(group)1  0.13553    0.10525   1.288   0.1983    
factor(group)2  0.25372    0.10878   2.332   0.0200 *  
factor(group)3  0.32132    0.10400   3.090   0.0021 ** 
log_count       0.37362    0.03757   9.945   <2e-16 ***
Q7_Q7_1        -0.03630    0.04638  -0.783   0.4341    
Q7_Q7_2         0.09941    0.04769   2.085   0.0375 *  
Q8_Q8_1         0.05860    0.04137   1.416   0.1571    
Q10            -0.01633    0.04067  -0.401   0.6882    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9145 on 602 degrees of freedom
Multiple R-squared:  0.1746,    Adjusted R-squared:  0.1636 
F-statistic: 15.92 on 8 and 602 DF,  p-value: < 2.2e-16

mod <- lm( log_relational_novelty ~ factor(group)/stage + log_count + Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10 , data = df)
summary(mod)

Call:
lm(formula = log_relational_novelty ~ factor(group)/stage + log_count + 
    Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.3715 -0.4255  0.2600  0.6158  1.5685 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)          -0.40812    0.18427  -2.215   0.0272 *  
factor(group)1        0.26337    0.25541   1.031   0.3029    
factor(group)2        0.11213    0.28738   0.390   0.6965    
factor(group)3        0.43797    0.25391   1.725   0.0851 .  
log_count             0.38109    0.03768  10.115   <2e-16 ***
Q7_Q7_1              -0.03506    0.04631  -0.757   0.4493    
Q7_Q7_2               0.09983    0.04762   2.097   0.0365 *  
Q8_Q8_1               0.05672    0.04131   1.373   0.1702    
Q10                  -0.01681    0.04060  -0.414   0.6790    
factor(group)0:stage  0.09163    0.06735   1.361   0.1742    
factor(group)1:stage  0.03993    0.06457   0.618   0.5365    
factor(group)2:stage  0.13611    0.07578   1.796   0.0730 .  
factor(group)3:stage  0.04475    0.06377   0.702   0.4832    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9131 on 598 degrees of freedom
Multiple R-squared:  0.1827,    Adjusted R-squared:  0.1663 
F-statistic: 11.14 on 12 and 598 DF,  p-value: < 2.2e-16

mod <- lm( log_relational_novelty ~ factor(group) * stage + log_count + Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10 , data = df)
summary(mod)

Call:
lm(formula = log_relational_novelty ~ factor(group) * stage + 
    log_count + Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.3715 -0.4255  0.2600  0.6158  1.5685 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)          -0.40812    0.18427  -2.215   0.0272 *  
factor(group)1        0.26337    0.25541   1.031   0.3029    
factor(group)2        0.11213    0.28738   0.390   0.6965    
factor(group)3        0.43797    0.25391   1.725   0.0851 .  
stage                 0.09163    0.06735   1.361   0.1742    
log_count             0.38109    0.03768  10.115   <2e-16 ***
Q7_Q7_1              -0.03506    0.04631  -0.757   0.4493    
Q7_Q7_2               0.09983    0.04762   2.097   0.0365 *  
Q8_Q8_1               0.05672    0.04131   1.373   0.1702    
Q10                  -0.01681    0.04060  -0.414   0.6790    
factor(group)1:stage -0.05169    0.09326  -0.554   0.5796    
factor(group)2:stage  0.04449    0.10118   0.440   0.6603    
factor(group)3:stage -0.04688    0.09276  -0.505   0.6135    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9131 on 598 degrees of freedom
Multiple R-squared:  0.1827,    Adjusted R-squared:  0.1663 
F-statistic: 11.14 on 12 and 598 DF,  p-value: < 2.2e-16

# Proposed model by stepwise regression
library(stats)
mod <- lm( log_relational_novelty ~ factor(group) + log_count + Q7_Q7_2 , data = df)
summary(mod)

Call:
lm(formula = log_relational_novelty ~ factor(group) + log_count + 
    Q7_Q7_2, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.2247 -0.4206  0.2416  0.6378  1.5600 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)    -0.18350    0.07530  -2.437  0.01510 *  
factor(group)1  0.13586    0.10467   1.298  0.19480    
factor(group)2  0.26234    0.10837   2.421  0.01578 *  
factor(group)3  0.32876    0.10377   3.168  0.00161 ** 
log_count       0.37742    0.03726  10.129  < 2e-16 ***
Q7_Q7_2         0.09265    0.03718   2.492  0.01296 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9141 on 605 degrees of freedom
Multiple R-squared:  0.1712,    Adjusted R-squared:  0.1644 
F-statistic:    25 on 5 and 605 DF,  p-value: < 2.2e-16

AIC(mod)

[1] 1632.175

BIC(mod)

[1] 1663.081

# without the factor ( group ) and with all confounding variables 
library(stats)
mod <- lm( log_relational_novelty ~ log_count + Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10 , data = df)
summary(mod)

Call:
lm(formula = log_relational_novelty ~ log_count + Q7_Q7_1 + Q7_Q7_2 + 
    Q8_Q8_1 + Q10, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.3412 -0.3826  0.2582  0.6443  1.4960 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.660e-16  3.724e-02   0.000   1.0000    
log_count    3.739e-01  3.764e-02   9.932   <2e-16 ***
Q7_Q7_1     -3.929e-02  4.651e-02  -0.845   0.3986    
Q7_Q7_2      1.070e-01  4.767e-02   2.244   0.0252 *  
Q8_Q8_1      6.659e-02  4.156e-02   1.602   0.1096    
Q10         -2.472e-02  4.049e-02  -0.611   0.5418    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9204 on 605 degrees of freedom
Multiple R-squared:  0.1597,    Adjusted R-squared:  0.1528 
F-statistic:    23 on 5 and 605 DF,  p-value: < 2.2e-16

AIC(mod)

[1] 1640.598

BIC(mod)

[1] 1671.504

library(stats)
mod.1 <- lm( log_relational_novelty ~ log_count + Q7_Q7_2 , data = df)
summary(mod.1)

Call:
lm(formula = log_relational_novelty ~ log_count + Q7_Q7_2, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.2719 -0.3984  0.2622  0.6406  1.4734 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.208e-16  3.724e-02   0.000  1.00000    
log_count    3.772e-01  3.731e-02  10.111  < 2e-16 ***
Q7_Q7_2      9.928e-02  3.731e-02   2.661  0.00799 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9205 on 608 degrees of freedom
Multiple R-squared:  0.1554,    Adjusted R-squared:  0.1527 
F-statistic: 55.95 on 2 and 608 DF,  p-value: < 2.2e-16

AIC(mod.1)

[1] 1637.722

BIC(mod.1)

[1] 1655.382

library(stats)
mod.2 <- lm( log_relational_novelty ~ factor(group) + log_count + Q7_Q7_2 , data = df)
summary(mod.2)

Call:
lm(formula = log_relational_novelty ~ factor(group) + log_count + 
    Q7_Q7_2, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.2247 -0.4206  0.2416  0.6378  1.5600 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)    -0.18350    0.07530  -2.437  0.01510 *  
factor(group)1  0.13586    0.10467   1.298  0.19480    
factor(group)2  0.26234    0.10837   2.421  0.01578 *  
factor(group)3  0.32876    0.10377   3.168  0.00161 ** 
log_count       0.37742    0.03726  10.129  < 2e-16 ***
Q7_Q7_2         0.09265    0.03718   2.492  0.01296 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9141 on 605 degrees of freedom
Multiple R-squared:  0.1712,    Adjusted R-squared:  0.1644 
F-statistic:    25 on 5 and 605 DF,  p-value: < 2.2e-16

AIC(mod.2)

[1] 1632.175

BIC(mod.2)

[1] 1663.081

# model with and without groups are very different ( significant )
anova(mod.1, mod.2)

Analysis of Variance Table

Model 1: log_relational_novelty ~ log_count + Q7_Q7_2
Model 2: log_relational_novelty ~ factor(group) + log_count + Q7_Q7_2
  Res.Df    RSS Df Sum of Sq      F   Pr(>F)   
1    608 515.18                                
2    605 505.54  3    9.6445 3.8473 0.009558 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

library(ALSM)

Loading required package: leaps
Loading required package: SuppDists
Loading required package: car
Loading required package: carData

step(lm(log_relational_novelty ~ factor(group) + log_count + Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10, data=df),
method="both", trace = 1 )

Start:  AIC=-100.24
log_relational_novelty ~ factor(group) + log_count + Q7_Q7_1 + 
    Q7_Q7_2 + Q8_Q8_1 + Q10

                Df Sum of Sq    RSS      AIC
- Q10            1     0.135 503.63 -102.081
- Q7_Q7_1        1     0.512 504.01 -101.623
<none>                       503.49 -100.244
- Q8_Q8_1        1     1.678 505.17 -100.211
- Q7_Q7_2        1     3.634 507.13  -97.850
- factor(group)  3     9.062 512.56  -95.345
- log_count      1    82.715 586.21   -9.308

Step:  AIC=-102.08
log_relational_novelty ~ factor(group) + log_count + Q7_Q7_1 + 
    Q7_Q7_2 + Q8_Q8_1

                Df Sum of Sq    RSS      AIC
- Q7_Q7_1        1     0.517 504.15 -103.454
- Q8_Q8_1        1     1.544 505.17 -102.211
<none>                       503.63 -102.081
- Q7_Q7_2        1     3.522 507.15  -99.823
- factor(group)  3     9.243 512.87  -96.968
- log_count      1    82.749 586.38  -11.132

Step:  AIC=-103.45
log_relational_novelty ~ factor(group) + log_count + Q7_Q7_2 + 
    Q8_Q8_1

                Df Sum of Sq    RSS      AIC
- Q8_Q8_1        1     1.393 505.54 -103.768
<none>                       504.15 -103.454
- Q7_Q7_2        1     3.164 507.31 -101.631
- factor(group)  3     9.349 513.49  -98.227
- log_count      1    83.685 587.83  -11.620

Step:  AIC=-103.77
log_relational_novelty ~ factor(group) + log_count + Q7_Q7_2

                Df Sum of Sq    RSS      AIC
<none>                       505.54 -103.768
- Q7_Q7_2        1     5.190 510.73  -99.527
- factor(group)  3     9.645 515.18  -98.221
- log_count      1    85.723 591.26  -10.064

Call:
lm(formula = log_relational_novelty ~ factor(group) + log_count + 
    Q7_Q7_2, data = df)

Coefficients:
   (Intercept)  factor(group)1  factor(group)2  factor(group)3       log_count         Q7_Q7_2  
      -0.18350         0.13586         0.26234         0.32876         0.37742         0.09265  

mod <- lm( log_relational_novelty ~ factor(group) + Q10 + Q8_Q8_1 + Q7_Q7_1 + Q7_Q7_2 , data = df)
summary(mod)

Call:
lm(formula = log_relational_novelty ~ factor(group) + Q10 + Q8_Q8_1 + 
    Q7_Q7_1 + Q7_Q7_2, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.1926 -0.4578  0.3261  0.7213  1.4289 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)   
(Intercept)    -0.20107    0.08126  -2.474  0.01362 * 
factor(group)1  0.20523    0.11322   1.813  0.07038 . 
factor(group)2  0.22874    0.11725   1.951  0.05154 . 
factor(group)3  0.35502    0.11207   3.168  0.00161 **
Q10             0.01822    0.04369   0.417  0.67679   
Q8_Q8_1         0.07857    0.04455   1.764  0.07827 . 
Q7_Q7_1        -0.06112    0.04993  -1.224  0.22137   
Q7_Q7_2         0.11639    0.05138   2.265  0.02386 * 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.986 on 603 degrees of freedom
Multiple R-squared:  0.039, Adjusted R-squared:  0.02785 
F-statistic: 3.496 on 7 and 603 DF,  p-value: 0.001099

Nest Phase in Group [ Linear Mixed Model ]

# convert to nominal factor
df$user2 = factor(df$user2)
df$stage = factor(df$stage)
df$group = factor(df$group)

# explore the data and their levels 
library(plyr)
ddply(df, ~ group * stage, function(data) summary(data$log_relational_novelty) )

ddply(df, ~ group * stage, summarise, log_relational_novelty.mean=mean(log_relational_novelty), log_relational_novelty.sd = sd(log_relational_novelty))

# histograms for two factors
hist(df[df$group == 0 & df$stage == 1,]$log_relational_novelty)

hist(df[df$group == 0 & df$stage == 2,]$log_relational_novelty)

hist(df[df$group == 0 & df$stage == 3,]$log_relational_novelty)

hist(df[df$group == 0 & df$stage == 4,]$log_relational_novelty)

hist(df[df$group == 1 & df$stage == 1,]$log_relational_novelty)

hist(df[df$group == 1 & df$stage == 2,]$log_relational_novelty)

hist(df[df$group == 1 & df$stage == 3,]$log_relational_novelty)

hist(df[df$group == 1 & df$stage == 4,]$log_relational_novelty)

hist(df[df$group == 2 & df$stage == 1,]$log_relational_novelty)

hist(df[df$group == 2 & df$stage == 2,]$log_relational_novelty)

hist(df[df$group == 2 & df$stage == 3,]$log_relational_novelty)

hist(df[df$group == 2 & df$stage == 4,]$log_relational_novelty)

hist(df[df$group == 3 & df$stage == 1,]$log_relational_novelty)

hist(df[df$group == 3 & df$stage == 2,]$log_relational_novelty)

hist(df[df$group == 3 & df$stage == 3,]$log_relational_novelty)

hist(df[df$group == 3 & df$stage == 4,]$log_relational_novelty)

boxplot(log_relational_novelty ~ group * stage, data = df, xlab="Group.Stage", ylab="log_relational_novelty")

with(df, interaction.plot(group, stage, log_relational_novelty, ylim=c(0, max(log_relational_novelty)))) # interaction plot

# library for LMM we will use on relational novelty 

library(lme4)
library(lmerTest)
library(car)

set sum-to-zero contrasts for the Anova cells

contrasts(df$group) <= "contr.sum"

     1    2    3
0 TRUE TRUE TRUE
1 TRUE TRUE TRUE
2 TRUE TRUE TRUE
3 TRUE TRUE TRUE

contrasts(df$stage) <= "contr.sum"

     2    3    4
1 TRUE TRUE TRUE
2 TRUE TRUE TRUE
3 TRUE TRUE TRUE
4 TRUE TRUE TRUE

# stage nested within group 
full.model = lmer( log_relational_novelty ~ group/stage + (1 | user2 ), data = df, REML = FALSE)
Anova(full.model, type=3, test.statistics="F")

Analysis of Deviance Table (Type III Wald chisquare tests)

Response: log_relational_novelty
              Chisq Df Pr(>Chisq)
(Intercept)  2.5598  1     0.1096
group        2.0162  3     0.5691
group:stage 11.8367 12     0.4589

full.model

Linear mixed model fit by maximum likelihood  ['lmerModLmerTest']
Formula: log_relational_novelty ~ group/stage + (1 | user2)
   Data: df
      AIC       BIC    logLik  deviance  df.resid 
1222.7027 1302.1745 -593.3514 1186.7027       593 
Random effects:
 Groups   Name        Std.Dev.
 user2    (Intercept) 0.8765  
 Residual             0.4483  
Number of obs: 611, groups:  user2, 157
Fixed Effects:
  (Intercept)         group1         group2         group3  group0:stage2  group1:stage2  group2:stage2  group3:stage2  
     -0.25894        0.15903        0.18673        0.31581       -0.01712        0.11397        0.03887        0.09815  
group0:stage3  group1:stage3  group2:stage3  group3:stage3  group0:stage4  group1:stage4  group2:stage4  group3:stage4  
      0.07843        0.13950        0.17836        0.16036        0.09115        0.10249        0.21386        0.13686  

library(performance)

check_collinearity(full.model)

# Check for Multicollinearity

Low Correlation

        Term  VIF   VIF 95% CI Increased SE Tolerance Tolerance 95% CI
       group 2.01 [1.80, 2.27]         1.42      0.50     [0.44, 0.55]
 group:stage 2.01 [1.80, 2.27]         1.42      0.50     [0.44, 0.55]

variability is very much higher in individual user and than in stages/phases for relational novelty. The remaining variability of 0.203502 comes from factor other than individual users and stage. factor(group)1 has higher relational novelty than group 0 by about 0.2099 . factor(group)3 has higher relational novelty than group 0 by about 0.3765.

var.model = lmer( log_relational_novelty ~ factor(group) + ( 1 | user2) + ( 1 | stage), data = df)
summary(var.model)

Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: log_relational_novelty ~ factor(group) + (1 | user2) + (1 | stage)
   Data: df

REML criterion at convergence: 1203.8

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.2978 -0.2484  0.0522  0.2410  3.5006 

Random effects:
 Groups   Name        Variance Std.Dev.
 user2    (Intercept) 0.789432 0.88850 
 stage    (Intercept) 0.002792 0.05284 
 Residual             0.203477 0.45108 
Number of obs: 611, groups:  user2, 157; stage, 4

Fixed effects:
               Estimate Std. Error       df t value Pr(>|t|)  
(Intercept)     -0.2208     0.1530 146.2072  -1.443    0.151  
factor(group)1   0.2099     0.2103 152.3350   0.998    0.320  
factor(group)2   0.2659     0.2097 154.1335   1.268    0.207  
factor(group)3   0.3765     0.2079 152.4574   1.812    0.072 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) fct()1 fct()2
factr(grp)1 -0.706              
factr(grp)2 -0.708  0.515       
factr(grp)3 -0.714  0.519  0.521

reduced.model = lm( log_relational_novelty ~ log_count + Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10, data = df)
summary(reduced.model)

Call:
lm(formula = log_relational_novelty ~ log_count + Q7_Q7_1 + Q7_Q7_2 + 
    Q8_Q8_1 + Q10, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.3412 -0.3826  0.2582  0.6443  1.4960 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.660e-16  3.724e-02   0.000   1.0000    
log_count    3.739e-01  3.764e-02   9.932   <2e-16 ***
Q7_Q7_1     -3.929e-02  4.651e-02  -0.845   0.3986    
Q7_Q7_2      1.070e-01  4.767e-02   2.244   0.0252 *  
Q8_Q8_1      6.659e-02  4.156e-02   1.602   0.1096    
Q10         -2.472e-02  4.049e-02  -0.611   0.5418    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9204 on 605 degrees of freedom
Multiple R-squared:  0.1597,    Adjusted R-squared:  0.1528 
F-statistic:    23 on 5 and 605 DF,  p-value: < 2.2e-16

full.model = lm( log_relational_novelty ~ factor(group) + log_count + Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10, data = df)
summary(full.model)

Call:
lm(formula = log_relational_novelty ~ factor(group) + log_count + 
    Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + Q10, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.2898 -0.4308  0.2405  0.6320  1.4916 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)    -0.17946    0.07540  -2.380   0.0176 *  
factor(group)1  0.13553    0.10525   1.288   0.1983    
factor(group)2  0.25372    0.10878   2.332   0.0200 *  
factor(group)3  0.32132    0.10400   3.090   0.0021 ** 
log_count       0.37362    0.03757   9.945   <2e-16 ***
Q7_Q7_1        -0.03630    0.04638  -0.783   0.4341    
Q7_Q7_2         0.09941    0.04769   2.085   0.0375 *  
Q8_Q8_1         0.05860    0.04137   1.416   0.1571    
Q10            -0.01633    0.04067  -0.401   0.6882    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9145 on 602 degrees of freedom
Multiple R-squared:  0.1746,    Adjusted R-squared:  0.1636 
F-statistic: 15.92 on 8 and 602 DF,  p-value: < 2.2e-16

anova(reduced.model, full.model)

Analysis of Variance Table

Model 1: log_relational_novelty ~ log_count + Q7_Q7_1 + Q7_Q7_2 + Q8_Q8_1 + 
    Q10
Model 2: log_relational_novelty ~ factor(group) + log_count + Q7_Q7_1 + 
    Q7_Q7_2 + Q8_Q8_1 + Q10
  Res.Df    RSS Df Sum of Sq      F  Pr(>F)  
1    605 512.56                              
2    602 503.49  3    9.0623 3.6117 0.01317 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

boxplot(log_relational_novelty~ stage*group,
col=c("white","lightgray", "blue", "green"),df)

check_collinearity(full.model)

# Check for Multicollinearity

Low Correlation

          Term  VIF   VIF 95% CI Increased SE Tolerance Tolerance 95% CI
 factor(group) 1.05 [1.01, 1.27]         1.03      0.95     [0.79, 0.99]
     log_count 1.03 [1.00, 1.48]         1.01      0.97     [0.67, 1.00]
       Q7_Q7_1 1.57 [1.42, 1.76]         1.25      0.64     [0.57, 0.70]
       Q7_Q7_2 1.66 [1.50, 1.87]         1.29      0.60     [0.54, 0.67]
       Q8_Q8_1 1.25 [1.16, 1.40]         1.12      0.80     [0.72, 0.87]
           Q10 1.21 [1.12, 1.35]         1.10      0.83     [0.74, 0.89]

library(car)

vif(full.model)

                  GVIF Df GVIF^(1/(2*Df))
factor(group) 1.053501  3        1.008724
log_count     1.029442  1        1.014614
Q7_Q7_1       1.568771  1        1.252506
Q7_Q7_2       1.658769  1        1.287932
Q8_Q8_1       1.248089  1        1.117179
Q10           1.206293  1        1.098314

vif(reduced.model)

log_count   Q7_Q7_1   Q7_Q7_2   Q8_Q8_1       Q10 
 1.020281  1.557734  1.635974  1.243664  1.180182 

library(multcomp)

Loading required package: mvtnorm
Loading required package: survival
Loading required package: TH.data
Loading required package: MASS

Attaching package: ‘TH.data’

The following object is masked from ‘package:MASS’:

    geyser

library(lsmeans)

Loading required package: emmeans
The 'lsmeans' package is now basically a front end for 'emmeans'.
Users are encouraged to switch the rest of the way.
See help('transition') for more information, including how to
convert old 'lsmeans' objects and scripts to work with 'emmeans'.

#summary(glht(full.model, lsm(pairwise ~ group / stage)), test = adjusted(type='holm'))